An Extended Cencov-Campbell Characterization of Conditional Information Geometry
This work offers a theoretical foundation for conditional models in information geometry, which is incremental but relevant for researchers in machine learning and statistics.
The paper extends the Cencov-Campbell axiomatic characterization to conditional information geometry, covering both normalized and nonnormalized cases, and shows that this provides a new axiomatic interpretation for logistic regression and AdaBoost.
We formulate and prove an axiomatic characterization of conditional information geometry, for both the normalized and the nonnormalized cases. This characterization extends the axiomatic derivation of the Fisher geometry by Cencov and Campbell to the cone of positive conditional models, and as a special case to the manifold of conditional distributions. Due to the close connection between the conditional I-divergence and the product Fisher information metric the characterization provides a new axiomatic interpretation of the primal problems underlying logistic regression and AdaBoost.